Bimodality of Plasma Glucose Distributions in Whites: A Bootstrap Approach to Testing Mixture Models

Abstract

The null distribution of the likelihood ratio test (LRT) of a onecomponent normal model versus two-component normal mixture model is unknown. In this paper, we take a bootstrap approach to the likelihood ratio test for testing bimodality of plasma glucose concentrations from Rancho Bernardo Diabetes Study. The small p-values from this approach support the hypothesis that a bimodal normal mixture model fits the data significantly better than a unimodal normal model. The size and power of the bootstrap based LRT are evaluated through simulations. The results suggest that a sample size of close to 500 would be necessary in order to attain a power of 90% for detecting the unbalanced mixtures with means and variances similar to those in the Rancho Bernardo data. Besides sample size, the power also depends on the two means and variances of the two components in the data.